I agree. My understanding is that swords were largely ceremonial or reserved for elite soldiers who were well trained. I have a hard time believing cheap bronze swords were available to the rank and file. Most soldiers fielded spears and shields and provided the anvil while cavalry with short spears or swords were the hammer.

Presumably swords were more effective from horseback than spears/lances until the invention of stirrups.

Swords were used by "runners", infantry that accompanied chariots. A sword and small shield was better for an isolated soldier; spears were useful for soldiers in close formation.

They probably did, but spear shafts get reused and the heads get melted down. A sword is much more labor-intensive and expensive to produce (not to mention harder to use effectively), so less likely to be recycled for it's constituents and more likely to be found in the archaeological record.